A boy is standing by the side of a railway track finds that an up train crosses him in 10 seconds and a down train of thrice the length of that of the up train crosses him in 15 seconds. How long (in seconds) will it take two trains to cross each other?

13\(\frac{1}{3}\)

LCM of [10 & 15] = 30

Let length of up train = 30m

 Length of down train = 30 × 3 = 90m

              Speed (up train) = \(\frac{30}{10}\) = 3 m/sec

          Speed (down train) = \(\frac{90}{15}\) = 6 m/sec  

  Time to cross each other = \(\frac{30 + 90}{3 + 6}\) = \(\frac{120}{9}\) = \(\frac{40}{3}\) = 13\(\frac{1}{3}\) second